The present invention relates to a method for optimizing holographic optical elements, hereinafter referred to as "HOE's".
In an optical system that is designed to operate with monochromatic or quasi-monochromatic illumination sources, it is possible to replace the conventional refractive elements with holographic optical elements (HOE's) that are based on diffractive optics. In general, the HOE's transform a given set of waves into another set of waves.
The increase in use of monochromatic radiation in complicated optical systems that require better optical performance and certain geometrical needs, has resulted in HOE's becoming very attractive. This is particularly true for systems operating in the far infrared (IR) radiation, for example 10.6 microns. In such systems, holographic elements that are based on diffractive optics have several advantages over conventional elements, in that they are thinner, more lightweight, and can perform operations that are impossible by other means.
There are many applications using CO.sub.2 lasers, operating at 10.6 microns wavelength, in which the HOE's are particularly useful. These include laser material processing, medical surgery, and infrared laser radars. For such applications, since there are no practical recording materials for far IR, the HOE's must be formed by using indirect recording. In practice, a computer generated mask, representing the grating function, is first plotted with a laser scanner, then reduced in size with optical demagnification, and finally recorded as a relief pattern with photolithographic techniques.
One of the main factors that have hindered the widespread use of diffractive elements for far IR radiation is that HOE's have relatively large amounts of aberrations. This is because the readout geometries and wavelengths are not identical to the recording geometry and wavelength. In order to minimize the aberrations, it is necessary to use optimization procedures for designing and recording a holographic element having a complicated grating function. Several optimization procedures have been proposed.
One known optimization procedure is based on numerical iterative ray-tracing techniques. This procedure, however, requires extensive calculations of ray directions, and the solutions often converge to local minima rather than to the desired absolute minimum.
Another known optimization procedure is based on minimizing the mean-squared difference of the phases of the actual and desired output wavefronts. In this procedure, the phase must be defined up to an additive constant so that the optimization procedure becomes rather complicated. It is therefore usually necessary to resort to approximate solutions.
As a result, such known optimization procedures do not yield an exact solution except in very specific cases.